Subjects algebra

Ap Fifth Term F852B3

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1. **State the problem:** We are given an arithmetic progression (A.P) where the first term $A$ is equal to twice the common difference $d$. We need to find the fifth term of this A.P. 2. **Recall the formula for the $n$th term of an A.P:** $$a_n = A + (n-1)d$$ where $a_n$ is the $n$th term, $A$ is the first term, and $d$ is the common difference. 3. **Given condition:** $$A = 2d$$ 4. **Find the fifth term $a_5$:** Substitute $n=5$ into the formula: $$a_5 = A + (5-1)d = A + 4d$$ 5. **Substitute $A = 2d$ into the expression:** $$a_5 = 2d + 4d = 6d$$ 6. **Interpretation:** The fifth term of the A.P is $6d$, which means it is six times the common difference. **Final answer:** $$\boxed{6d}$$